Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling

• URL: http://arxiv.org/abs/2505.16481v1
• Date: Thu, 22 May 2025 10:07:33 GMT
• Title: Neighbour-Driven Gaussian Process Variational Autoencoders for Scalable Structured Latent Modelling
• Authors: Xinxing Shi, Xiaoyu Jiang, Mauricio A. Álvarez,
• Abstract summary: Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior.<n> performing exact GP inference in large-scale GPVAEs is computationally prohibitive, often forcing existing approaches to rely on restrictive kernel assumptions.<n>We propose a neighbour-driven approximation strategy that exploits local adjacencies in the latent space to achieve scalable GPVAE inference.
• Score: 14.358070928996069
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP inference in large-scale GPVAEs is computationally prohibitive, often forcing existing approaches to rely on restrictive kernel assumptions or large sets of inducing points. In this work, we propose a neighbour-driven approximation strategy that exploits local adjacencies in the latent space to achieve scalable GPVAE inference. By confining computations to the nearest neighbours of each data point, our method preserves essential latent dependencies, allowing more flexible kernel choices and mitigating the need for numerous inducing points. Through extensive experiments on tasks including representation learning, data imputation, and conditional generation, we demonstrate that our approach outperforms other GPVAE variants in both predictive performance and computational efficiency.

Related papers

• Distributional encoding for Gaussian process regression with qualitative inputs [0.7342677574855652]
  We show that a generalization based on distributional encoding (DE) makes use of all samples of the target variable for a category.<n>Our approach is validated empirically, and we demonstrate state-of-the-art predictive performance on a variety of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2025-06-05T09:35:02Z)
• Tighter sparse variational Gaussian processes [22.290236192353316]
  Sparse variational Gaussian process (GP) approximations have become the de facto standard for scaling GPs to large datasets.<n>This paper introduces a provably tighter variational approximation by relaxing the standard assumption that the conditional approximate posterior given the inducing points must match that in the prior.
  arXiv  Detail & Related papers  (2025-02-07T08:33:28Z)
• Robust Gaussian Processes via Relevance Pursuit [17.39376866275623]
  We propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels.<n>We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances.
  arXiv  Detail & Related papers  (2024-10-31T17:59:56Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Robust and Adaptive Temporal-Difference Learning Using An Ensemble of Gaussian Processes [70.80716221080118]
  The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning. The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs. To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
  arXiv  Detail & Related papers  (2021-12-01T23:15:09Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Incremental Ensemble Gaussian Processes [53.3291389385672]
  We propose an incremental ensemble (IE-) GP framework, where an EGP meta-learner employs an it ensemble of GP learners, each having a unique kernel belonging to a prescribed kernel dictionary. With each GP expert leveraging the random feature-based approximation to perform online prediction and model update with it scalability, the EGP meta-learner capitalizes on data-adaptive weights to synthesize the per-expert predictions. The novel IE-GP is generalized to accommodate time-varying functions by modeling structured dynamics at the EGP meta-learner and within each GP learner.
  arXiv  Detail & Related papers  (2021-10-13T15:11:25Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• Cauchy-Schwarz Regularized Autoencoder [68.80569889599434]
  Variational autoencoders (VAE) are a powerful and widely-used class of generative models. We introduce a new constrained objective based on the Cauchy-Schwarz divergence, which can be computed analytically for GMMs. Our objective improves upon variational auto-encoding models in density estimation, unsupervised clustering, semi-supervised learning, and face analysis.
  arXiv  Detail & Related papers  (2021-01-06T17:36:26Z)
• Scalable Gaussian Process Variational Autoencoders [17.345687261000045]
  We propose a new scalable GP-VAE model that outperforms existing approaches in terms of runtime and memory footprint, is easy to implement, and allows for joint end-to-end optimization of all components.
  arXiv  Detail & Related papers  (2020-10-26T10:26:02Z)
• Sparse Gaussian Process Variational Autoencoders [24.86751422740643]
  Existing approaches for performing inference in GP-DGMs do not support sparse GP approximations based on points. We develop the sparse Gaussian processal variation autoencoder (GP-VAE) characterised by the use of partial inference networks for parameterising sparse GP approximations.
  arXiv  Detail & Related papers  (2020-10-20T10:19:56Z)
• Likelihood-Free Inference with Deep Gaussian Processes [70.74203794847344]
  Surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. We propose a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases.
  arXiv  Detail & Related papers  (2020-06-18T14:24:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.